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Bayes linear spaces
Van den Boogaart, Karl Gerard; Egozcue Rubí, Juan José; Pawlowsky-Glahn, Vera
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. NRG - Riscos Naturals i Geoestadística
Linear spaces consisting of $\sigma$-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
Exponential families (Statistics)
Probability measures
Vector spaces
Famílies exponencials (Estadística)
Probabilitats, Mesures de
Espais vectorials
Classificació AMS::60 Probability theory and stochastic processes::60A Foundations of probability theory
Classificació AMS::62 Statistics::62E Distribution theory

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